David Cameron could face another inquiry in the wake of the cash-for-access affair after the cabinet secretary was asked to investigate whether the prime minister had broken the rules by allowing the use of Downing Street for political activities.

Labour has asked Sir Jeremy Heywood, who oversees the ministerial code, to examine why a dinner for donors was held on public property, and why the Conservative party chairman, Lord Feldman, reportedly has a permanent desk at No 10.

The complaint from Jon Trickett, the shadow minister for the Cabinet Office, will extend a saga the government has taken great efforts to try to close down.

The Conservatives are investigating comments by Peter Cruddas, who resigned as party treasurer after being recorded saying donors could pay for private dinners with Cameron and make suggestions on policy. But Labour has called for an independent investigation.

The Electoral Commission and the police have been asked to investigate comments made by Sarah Southern, a former Cameron adviser turned lobbyist, who was recorded telling undercover reporters posing as foreign donors that they could make donations through proxy donors or UK companies to circumvent donation laws.

In a letter to Heywood, Trickett wrote that the prime minister held a thank you dinner for donors after the general election downstairs in No 10, not at the prime minister's private flat.

Trickett wrote: "It is clear that at least one dinner took place in Downing Street but not in the private flat. That means that a party fundraising dinner occurred on government property that was not an official residence – suggesting a breach of the ministerial code."

The Tories have confirmed the dinner was not held in the prime minister's private residence, but say the flat was being refurbished at the time.

A second part of the complaint refers to a report in the Daily Mail on Tuesday that Lord Feldman had been given office space in 10 Downing Street and met donors there "when he chooses". Trickett said Feldman, a close friend of Cameron, should not be allowed to conduct party business on government premises.

"Given that the ministerial code is clear that government facilities provided for ministers to carry out official duties should not be used for party activities, I would be grateful for an explanation of why Conservative party chairman Lord Feldman has been given access to and desk space in Downing Street for what are narrowly Conservative party matters including fundraising," Trickett wrote.

A Downing Street source said the allegation that Feldman has a desk in the building was "not true". A Cabinet Office spokesperson said they would respond once the complaint had been read.